from one point to another. At the middle of one of the swollen portions, or ãbeads,ã the two curvatures are both positive; the expression (1ã₤ãã₤ R ã₤+ã₤1ã₤ãã₤ Rÿ£¢ãý ) is therefore positive, and it is also finite. The film, accordingly, exercises a positive tension inwards, which must be compensated by a finite and positive outward pressure P . At the middle of one of the narrow necks, between two adjacent beads, there is obviously, in the transverse direction, a much stronger curvature than in the former case, and the curvature which balances it is now a negative one. But the sum of the two must remain positive, as well as constant; and we therefore see that the convex or positive curvature must always be greater than the concave or negative curvature at the same point. This is plainly the case in our figure of the unduloid.
The nodoid is, like the unduloid, a continuous curve which keeps altering its curvature as it alters its distance from the axis; but in this case the resultant pressure inwards is negative instead of positive. But this curve is a complicated one, and a full discussion of it would carry us beyond our scope.
In one of Plateauãs experiments, a bubble of oil (protected from gravity by the specific gravity of the surrounding fluid being identical with its own) is balanced between two annuli. It may then be brought to assume the form of Fig. 63, that is to say the form of a cylinder with spherical ends; and there